
Re: Simplified Twin Paradox Resolution.
Posted:
Jan 6, 2013 9:25 AM


On Jan 6, 11:23 am, Sylvia Else <syl...@not.at.this.address> wrote: > On 6/01/2013 3:59 PM, Koobee Wublee wrote: > > > > > > > > > > > On Jan 5, 5:57 pm, Sylvia Else wrote: > >> On 5/01/2013 5:59 AM, Koobee Wublee wrote: > > >>> Instead of v, let?s say (B = v / c) for simplicity. The earth is > >>> Point #0, outbound spacecraft is Point #1, and inbound spacecraft is > >>> Point #2. > > >>> According to the Lorentz transform, relative speeds are: > > >>> ** B_00^2 = 0, speed of #0 as observed by #0 > >>> ** B_01^2 = B^2, speed of #1 as observed by #0 > >>> ** B_02^2 = B^2, speed of #2 as observed by #0 > > >>> ** B_10^2 = B^2, speed of #0 as observed by #1 > >>> ** B_11^2 = 0, speed of #1 as observed by #1 > >>> ** B_12^2 = 4 B^2 / (1 ? B^2), speed of #2 as observed by #1 > > >>> ** B_20^2 = B^2, speed of #0 as observed by #2 > >>> ** B_21^2 = 4 B^2 / (1 ? B^2), speed of #1 as observed by #2 > >>> ** B_22^2 = 0, speed of #2 as observed by #2 > > >>> When Point #0 is observed by all, the Minkowski spacetime (divided by > >>> c^2) is: > > >>> ** dt_00^2 (1 ? B_00^2) = dt_10^2 (1 ? B_10^2) = dt_20^2 (1 ? B_20^2) > > >>> When Point #1 is observed by all, the Minkowski spacetime (divided by > >>> c^2) is: > > >>> ** dt_01^2 (1 ? B_01^2) = dt_11^2 (1 ? B_11^2) = dt_21^2 (1 ? B_21^2) > > >>> When Point #2 is observed by all, the Minkowski spacetime (divided by > >>> c^2) is: > > >>> ** dt_02^2 (1 ? B_02^2) = dt_12^2 (1 ? B_12^2) = dt_22^2 (1 ? B_22^2) > > >>> Where > > >>> ** dt_00 = Local rate of time flow at Point #0 > >>> ** dt_01 = Rate of time flow at #1 as observed by #0 > >>> ** dt_02 = Rate of time flow at #2 as observed by #0 > > >>> ** dt_10 = Rate of time flow at #0 as observed by #1 > >>> ** dt_11 = Local rate of time flow at Point #1 > >>> ** dt_12 = Rate of time flow at #2 as observed by #1 > > >>> ** dt_20 = Rate of time flow at #0 as observed by #2 > >>> ** dt_21 = Rate of time flow at #1 as observed by #2 > >>> ** dt_22 = Local rate of time flow at Point #2 > > >>> So, with all the pertinent variables identified, the contradiction of > >>> the twins? paradox is glaring right at anyone with a thinking brain. > >>> <shrug> > > >> You assert that there are a paradox. I take it you mean in the sense > >> that the theory gives two results for one situation, such that they are > >> impossible to reconcile. > > >> I challenge you to show that mathematically, rather than just asserting > >> it. Do not just point at the maths above and claim that it's obvious. > > > PD, are you turning into a troll now? For the n?th time, the > > following is one such presentation of mathematics that show the > > contradiction in the twins? paradox. > > >    > > > From the Lorentz transformations, you can write down the following > > equation per Minkowski spacetime. Points #1, #2, and #3 are > > observers. They are observing the same target. > > > ** c^2 dt1^2 ? ds1^2 = c^2 dt2^2 ? ds2^2 = c^2 dt3^2 ? ds3^2 > > > Where > > > ** dt1 = Time flow at Point #1 > > ** dt2 = Time flow at Point #2 > > ** dt3 = Time flow at Point #3 > > > ** ds1 = Observed target displacement segment by #1 > > ** ds2 = Observed target displacement segment by #2 > > ** ds3 = Observed target displacement segment by #3 > > > The above spacetime equation can also be written as follows. > > > ** dt1^2 (1 ? B1^2) = dt2^2 (1 ? B2^2) = dt3^2 (1 ? B3^2) > > > Where > > > ** B^2 = (ds/dt)^2 / c^2 > > > When #1 is observing #2, the following equation can be deduced from > > the equation above. > > > ** dt1^2 (1 ? B1^2) = dt2^2 . . . (1) > > > Where > > > ** B2^2 = 0, #2 is observing itself > > > Similarly, when #2 is observing #1, the following equation can be > > deduced. > > > ** dt1^2 = dt2^2 (1 ? B2^2) . . . (2) > > > Where > > > ** B1^2 = 0, #1 is observing itself > > > According to relativity, the following must be true. > > > ** B1^2 = B2^2 > > > Thus, equations (1) and (2) become the following equations > > respectively. > > > ** dt1^2 (1 ? B^2) = dt2^2 . . . (3) > > ** dt2^2 = dt1^2 (1 ? B^2) . . . (4) > > > Where > > > ** B^2 = B1^2 = B2^2 > > > The only time the equations (3) and (4) can coexist is... > > ... never > > In deriving [1] and [2] you prefaced them with caveats about who is > observing whom. So they relate to different measurement situations. You > cannot combine them in any meaningful way. > > Sylvia.
Nobody is observing anybody. Everybody has right to write down equations.

